The full expressions (REF ) to (REF ) can be rewritten in terms of the flavor octet baryon-meson couplings \(D\) , \(F\) , \(\mathcal {C}\) , and \(\mathcal {H}\)  introduced in Refs. [1]}, [2]}, which are related to the coefficients of the \(1/N_c\)  expansion \(a_1\) , \(b_2\) , \(b_3\) , and \(c_3\)  at \(N_c=3\) . The relations are [3]}
\(& & D = \frac{1}{2} a_1 + \frac{1}{6} b_3, \\& & F = \frac{1}{3} a_1 + \frac{1}{6} b_2 + \frac{1}{9} b_3, \\& & \mathcal {C} = - a_1 - \frac{1}{2} c_3, \\& & \mathcal {H} = - \frac{3}{2} a_1 - \frac{3}{2} b_2 - \frac{5}{2} b_3.\) 
